Answer to Question #143949 in Macroeconomics for Tanvir Alam

Question

Consider an economy described by the equations of the
Solow-model (without technological or population growth), except that all labor income
is consumed and all other income is saved. The production function is Cobb-Douglas,
so f(k(t)) = k(t)α.
1. Write down the equation that governs capital accumulation!
2. Does this economy converge to a steady-state? If so, what is the steady state level
of k. How does that compare to the level derived in the lecture notes?
3. Is the saving rate in the economy constant? Increasing? Decreasing? What is the
intuition for that?

Answer 1

1. f(k(t)) = αk(t).

2.there is a single level of capital strength at which investment equals depreciation. If the economy reaches this level, it will not change over time, since the two forces acting on it (investment and retirement) are precisely balanced

$\Delta$ k=0

3.Higher savings lead to faster growth, but this acceleration doesn't last forever. An increase in the savings rate ensures growth until the economy reaches a new sustainable state. If the economy maintains a high rate of savings, both capital and productivity will be high, but it will not be possible to maintain high rates of economic growth forever.

Solow's basic model shows that capital accumulation alone cannot explain continuous economic growth. A high level of savings temporarily increases the growth rate, but the economy eventually approaches a stable state in which capital reserves and output are constant. In order to explain the continuous economic growth that is observed in most countries of the world, it is necessary to expand the Solow model to include two other sources of economic growth: population growth and technological progress.